How do the bubble oscillations in two-phase flows affect the dissipation rate of turbulent kinetic energy?

Question

I am investigating the effects of bubble oscillations (calculated using the Rayleigh-Plesset equation for bubble dynamics) on the turbulence in two-phase flows. Since I am using cryogenic fluids, the thermal effects also play a role. I am trying to determine the connection between the oscillation frequencies and how they influence the turbulence dissipation rate.

I guess that when the frequencies are high, i.e., when the liquid-vapour interface oscillates at high frequencies, the turbulent kinetic energy in the flow increases. So, will the dissipation rate also increase proportionally to the turbulent kinetic energy? (epsilon proportional to k^1.5)

Answer 1

I remember doing something alike but with solids in oil pipes... As it turns out in a quick search in google I found the thesis is now published online by Arizona State University.

The oscillation is given in this model by a WENO equation even though the meaning of WENO is Weighted Essentially Non Oscillatory.

So the idea is this, you divide the pipe system in many small cells in three levels, the last level is defined to be either one phase or the other. Here comes the interesting part; The G(x) parameter (can't remember the name but it is on the documentation for sure) is defined to solve the interphase.

If you have any trouble compiling the software I would gladly help, I had to debug some of it as part of my social services.

https://repository.asu.edu/items/34792

Answer 2

An interesting question

" I am trying to find out the connection between the oscillation frequencies and how they influence the turbulence dissipation rate."

I'm not familiar with bubble mechanics, but all materials that can conduct a mechanical wave (sound) have three important properties: the speed of the wave, acoustic dampening, and compressibility, the more dense a material is (down to a limit) speed increase (and therefore the frequency gets lower), this is also highly dependent on the temperature (compressibility and energy already present in the material), a bubble in a cryogenic fluid would get a slower speed and a much higher frequency than expected. The fluid would also have very different acoustic dampening as a fluid or gas. In a gas phase its a lot higher, so the wave exiting the bubble (not taking reflected energy into account) would be lower hitting the next in any vector. Dampening is also frequency and temperature dependent. Just some thoughts.

I hope this helps in some way.

Answer 3

The investigation you're conducting on bubble oscillations and their influence on turbulence in two-phase flows, especially with cryogenic fluids, involves multiple factors that interconnect fluid dynamics, thermodynamics, and turbulence theory. Here's a structured approach to understanding the connection between oscillation frequencies and turbulence dissipation rate:

1. Rayleigh-Plesset Equation (RPE) and Bubble Oscillations: The Rayleigh-Plesset equation describes the dynamics of a spherical bubble in a liquid, taking into account the balance of forces acting on the bubble surface

In cryogenic fluids, temperature effects significantly modify the bubble oscillation frequencies due to changes in viscosity, density, surface tension, and vapor pressure.

2. Bubble Oscillations and Turbulence: Oscillation Frequencies:The oscillation frequency of the bubble is a key factor in energy transfer to the surrounding liquid. In two-phase flows, bubbles inject energy into the flow via periodic expansions and contractions, which can either enhance or suppress turbulence. Resonant Frequencies: When the oscillation frequency of the bubbles is in resonance with natural frequencies in the flow, they can amplify turbulence generation and transfer energy more effectively into turbulent eddies. Non-Resonant Frequencies: When out of resonance, the interaction is weaker, leading to less pronounced turbulence production.

3. Influence on Turbulence Dissipation Rate: The turbulence dissipation rate is the rate £ at which turbulent kinetic energy is converted into heat due to viscous forces. For bubble-induced turbulence, the oscillations influence the generation and dissipation of turbulent eddies, especially near the bubble-liquid interface. High-Frequency Oscillations:High-frequency oscillations generate smaller eddies, leading to higher dissipation rates as energy is more rapidly cascaded down to smaller scales. Low-Frequency Oscillations:** Lower-frequency oscillations generate larger eddies, leading to slower cascades and lower dissipation rates.

4. Thermal Effects in Cryogenic Fluids:

• Thermal Fluctuations: In cryogenic conditions, thermal fluctuations significantly impact the bubble dynamics by altering the vapor pressure inside the bubbles. This results in changes to the oscillation amplitude and frequency, which in turn modifies the turbulence structure. Heat Transfer Coupled with Turbulence:The interaction between heat transfer and turbulence becomes more pronounced in cryogenic fluids. Thermal effects can lead to stronger oscillation-induced turbulence or suppress turbulence if the thermal gradients are large enough to cause phase changes (e.g., evaporation or condensation around the bubble).

5. Practical Steps to Determine the Influence:** -Oscillation Frequency Analysis:Use the RPE to calculate the oscillation frequencies of bubbles for different conditions (e.g., pressure, temperature) in the cryogenic fluid. Turbulence Modeling: Incorporate these frequencies into a turbulence model (e.g., k-£ or LES models) to study how different oscillation modes affect the turbulence dissipation rate. Coupling with Thermal Effects: Use a coupled thermal-fluid simulation (or an extended RPE with thermal effects) to account for the temperature dependency of viscosity, surface tension, and density, and observe their influence on turbulence dissipation.

By analyzing the frequency response of bubbles in cryogenic conditions and their energy transfer to the turbulent flow, you can better understand how oscillations modulate the turbulence dissipation rate. This requires careful consideration of both fluid properties (which vary strongly with temperature) and oscillation dynamics.